The machine therefore has a first machine part and a second machine part, and the second machine part can be rotated relative to the first machine part about an axis of rotation. Data signals are optically transmitted, i.e. an optical signal transmitting device is disposed on one machine part and a device for receiving optical signals is disposed on the other machine part. It is rarely possible to dispose an optical transmitter and an optical receiver precisely in the axis of rotation. If optical signals are now to travel from an optical transmitter to an optical receiver outside of the axis of rotation, the problem is that the optical signals must be transmitted at any angular positions of the second machine part. This problem has hitherto been solved by providing a plurality of light sources and ensuring by constructional means that the light rays emitted by the light sources spread out to form a luminous ring at a particular location in the machine. The optical receiver can be a point detector. When the rotating machine part rotates, it is then always ensured that light passes from the optical transmitter to the optical receiver.